1. Field of the Invention
The present invention relates to the field of signal processing and control systems. More particularly, the present invention relates to the dynamic optimization of time varying trajectories to make signal processing and control systems achieve desired outcomes.
2. Background Information
Signal processing and the control of physical systems generally involves obtaining measurements from a physical system in the form of electrical signals and processing the signals in order to bring about a desired result. For example, the control of a physical system typically involves obtaining measurements from the physical system, comparing the measurements with a predetermined control recipe, and adjusting the system inputs, all in real time, in response to the comparison to minimize variations between the measured values and recipe values. During signal processing and control, the signals to be processed or the variables to be controlled are not always directly available for observation and must be inferred from indirect and noisy measurements. The indirect measurements are generally obtained from embedded sensors which contain multiple pieces of information that are dynamically confounded. Extraction of the information of interest requires the use of complex and time consuming calibration procedures and the use of estimating techniques that result in high computation costs. Equipment setup costs are also high since diagnostic measurements must be taken to correlate measured signals to indirect measurements for each piece of equipment.
In some physical systems there are variables which cannot be measured during operation but which affect the ultimate outcome of the system. Thus, some unmonitorable variable (or variables) affect the final system output.
In addition, the measurements that are available from a physical system are not always obtainable at a single time interval (time scale). For example, there may be a first measurement that is obtainable only at a first time scale, a second measurement that is only obtainable at a second time scale, a third measurement that is only obtainable at a third time scale, and so on.
Further, the ultimate variable (or variables) of interest are often only available at a coarse time scale (i.e. a slow rate, for example after each run is completed). In a process for depositing a film on a semiconductor wafer, the thickness of the film deposited cannot be directly measured until the run (or process) is finished.
Moreover, some continuous processes also have variables that must be measured at two or more different time scales. Such variables are sometimes only available at a course time scale and these variables are often the variables that need to be controlled. In a process for controlling the peak power demand in a captive electric generator connected to a power distribution grid, the peak power demand value cannot be directly measured until a set time interval has elapsed.
Often, the task of controlling a system involves not only the control of a single physical system, but the control of a family of similar but not identical physical systems. This situation is most prevalent in high volume manufacturing applications. The characteristics of a single physical system tend to change over time due to equipment degradation and other causes. Moreover, the characteristics of members of a family of physical systems tend to differ from one physical system to another due to equipment manufacturing variations. It is important to account for these differences so that the signal processing or control system may be updated accordingly. Otherwise, the accuracy of the signal processing or control system is compromised.
Current signal processing and control systems do not provide for the rapid calibration of such systems, nor do they provide for the rapid computation of time varying control trajectories to optimize the performance of these systems.
There are a number of related control methods that are collectively known as Model Predictive Control (MPC). MPC computes an optimal trajectory over a finite, but usually long, time interval. The first part (in time) of the optimal trajectory is applied to a system for an interval much shorter than the full time interval and the remaining portion of the optimal trajectory is discarded. In MPC the optimal trajectory applied during the short time period to the system is held constant. At the end of that short time interval, the process is repeated for a second part (in time), i.e., where the first part left off. This process is repeated indefinitely, or as many times as is desired in a continuous process. MPC methods provide continuing control at a single time scale (determined by the short time interval).
Thus, what is needed is an accurate and cost efficient method and apparatus for processing signals generated within a physical system, or family of physical systems, that allow the modification and control of time varying trajectories to optimize the performance of the physical system at different time scales in the face of the issues described above.